When extracting spectral information from a radiation source, Fourier transform spectroscopy is often used. One technique used in Fourier transform spectroscopy involves using a Michelson interferometer, in which the amplitude of a collected wavefront is divided into two wavefronts, which are interfered to form an interference pattern. The optical path length of one of the wavefronts is varied to permit the collection of intensity information from a number of interference patterns formed by the two wavefronts. This intensity information is then Fourier transformed to extract spectral information from the wavefront. Because the entire collected wavefront is interfered with itself, the Fourier transform contains all the spatial frequencies contained in the optical transfer function (“OTF”) of the system (which is given by the auto-correlation of the pupil function of the collecting elements of the system). The use of a Michelson interferometer to collect spectral information experiences several drawbacks, however. For example, the spectral bandwidth of the system is limited by the beamsplitter which divides the collected wavefront. Further, because the OTF is wavelength dependent, the spectral data obtained by the Fourier transform varies from the object spectrum.
Another approach to Fourier transform spectroscopy involves using a Fizeau interferometer, in which separate portions of a collected wavefront are interfered with each other to form interference patterns on an image plane. As the optical path length of one of the separate portions of the collected wavefront is changed, a phase delay is introduced between the portions, causing interference patterns to translate across the image plane. These interference patterns are Fourier transformed to extract spectral fringe visibility data for all field points. Because separate portions of the collected wavefront are interfered in a Fizeau Fourier transform spectrometer (“FFTS”), only those spatial frequencies modulated by the spectral optical transfer function (“SOTF”) of the system (which is given by the cross-correlation of the pupil functions of the elements used to collect the separate portions of the collected wavefront) are present in the Fourier transform. Further, because the SOTF is given by the cross-correlation of separate apertures, all low spatial frequency (“DC”) information is missing from the Fourier transform.
Accordingly, there is a need for a method to restore both the DC information and the spectral information related to low spatial frequency components of an image obtained with an FFTS. The present invention satisfies these needs and provides other advantages as well.